模态逻辑系统S4中的度量结构

doi:10.6040/j.issn.1671-9352.0.2015.135

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (2): 108-113.doi: 10.6040/j.issn.1671-9352.0.2015.135

模态逻辑系统S4中的度量结构

龚加安,吴洪博^*

陕西师范大学数学与信息科学学院, 陕西西安 710062

收稿日期:2015-03-30 出版日期:2016-02-16 发布日期:2016-03-11
通讯作者: 吴洪博(1959— ),男,博士,教授,研究方向为格上拓扑与模糊推理. E-mail:wuhb@snnu.edu.cn E-mail:sxslgongke@163.com
作者简介:龚加安(1975— ),男,硕士,研究方向为格上拓扑与模糊推理. E-mail:sxslgongke@163.com
基金资助:
国家自然科学基金重点项目(11531009);国家自然科学基金面上项目(61572016)

Metric structure in modal logic system S4

GONG Jia-an, WU Hong-bo^*

School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China

Received:2015-03-30 Online:2016-02-16 Published:2016-03-11

摘要/Abstract

摘要： 在模态逻辑S4中通过有限模型建立了模态公式的(n)真度理论,研究了模态逻辑S4中命题的(n)真度的性质。提出了模态公式间的(n)相似度理论,并由此在全体公式集中,建立了(n)伪距离, 得出了(n)模态逻辑S4的度量空间,该空间以经典逻辑度量空间为子空间,提出了一种模态逻辑S4中近似推理的框架。

关键词: (n)真度, 模态逻辑, 近似推理

Abstract: The theory of(n)truth degrees of formulas is proposed in modal logic system S4. Some properties of(n)truth are investigated in modal logic system S4. The theory of(n)similarity degrees among modal formulas is proposed and a pseudo-metric is defined thereform on the set of all formulas. The(n)modal logic metric space is derived therefrom which contains the classical logic metric space as a subspace. Finally, a kind of approximate reasoning theory is proposed in modal logic system S4.

Key words: modal logic, (n)truth degrees, approximate reasoning

中图分类号:

O141.1

龚加安,吴洪博. 模态逻辑系统S4中的度量结构[J]. 山东大学学报（理学版）, 2016, 51(2): 108-113.

GONG Jia-an, WU Hong-bo. Metric structure in modal logic system S4[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(2): 108-113.

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模态逻辑系统S4中的度量结构

Metric structure in modal logic system S4

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